Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On commuting families of nonexpansive operators

Author: Gideon Schechtman
Journal: Proc. Amer. Math. Soc. 84 (1982), 373-376
MSC: Primary 47H09; Secondary 47H10
MathSciNet review: 640234
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For each $ n$, $ 1 \leqslant n \leqslant \infty $, there exist a weakly compact, convex subset $ W$ of $ {L_1}$ and a family $ \{ {T_i}\} _{i = 1}^n(\{ {T_i}\} _{i = 1}^\infty {\text{ in case }}n = \infty )$ of nonexpansive operators of $ W$ into $ W$ such that there is no common fixed point for the whole family but any (finite) strict subfamily admits a common fixed point.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H09, 47H10

Retrieve articles in all journals with MSC: 47H09, 47H10

Additional Information

PII: S 0002-9939(1982)0640234-3
Keywords: Common fixed point, nonexpansive operators, weakly compact sets, convex sets
Article copyright: © Copyright 1982 American Mathematical Society